Rolling Without Slipping and Pulleys

A very large number of the mechanical energy conservation problems we will do involve the relation we discussed previously that relates rotational motion to linear motion. Specifically we will apply this to what is referred to as rolling without slipping, or perfect rolling. There are two reasons this is an important condition to understand:

When two surfaces slip across each other, thermal energy is the result. So when an object rolls without slipping, there may be static friction present, but there is no kinetic friction, which means that no thermal energy is produced and mechanical energy is conserved.

When a round object rolls perfectly, the distance it travels in a straight line is directly related to the angle through which it rotates.

We’ll keep the first observation in mind for later, but right now let’s focus on the second condition: